Relating fractions to 1

We are told to select the two fractions that are greater than one, so pause this video and see if you can figure out which two of these fractions are greater than one.

All right, now let's work on this together. The main realization here, the main thing to pay attention to, is how the numerator relates to the denominator. When we are at one, they're equal to each other. For example, one is equal to one whole. I guess you could write it that way: one, once. You could also write it as two halves, which is also equal to three thirds, which is also equal to four fourths. We could go on and on if we wanted. In terms of six, one would be equal to six sixths.

So, if whatever we have up here is larger than the denominator, we are greater than one. For instance, if we have seven sixths, or if we were to have maybe five fourths, notice the numerator is larger than the denominator. These are all situations when we are greater than one. In contrast, all the situations where the numerator is less than the denominator, like one-half or nine elevenths or ten elevenths, are all situations where we are less than one. Oh, this is less than one.

So, let's look over here. Four is less than six. Four sixths is less than six sixths. Remember, one is the same thing as six sixths. So, this is not greater than one, so I would not select that. Nine fourths, well, that's definitely larger than four fourths; that is greater than one. Once again, our numerator is larger than our denominator, so we know that we are greater than one. So, I will select that one.

Then we see again five halves. Two halves is equal to one, so five halves is definitely greater than one. I like that one as well, and notice five is greater than two. We already know we picked our two choices, but we can look at the other ones. Seven is less than eight, so seven eighths is less than eight eighths. So this is less than one, and three thirds, we've already talked about it; that's equal to one. So I like those two choices.

Let's do another example that tackles it a little bit of a different way. It says, which fraction could represent point A on the number line? Point A is here. They don't tell us a lot about point A, but all they do tell us by looking at the number line is that point A is less than one. So, which of these is another way to think about it as less than one?

All right, in order for it to be less than one, the numerator has to be less than the denominator. Here, our numerator is greater than the denominator. Seven fourths is definitely larger than four fourths. Remember, four fourths is equal to one. This right over here, I could rewrite as four fourths. So, seven fourths is going to be someplace over there, so this is definitely not our choice.

Two halves, well, once again that's the same thing as one. That's right over there, so that's not our choice. What about five eighths? Well, five eighths, the numerator is less than the denominator. Eight eighths is equal to one, so that's that point again. Therefore, five eighths would be to the left of that, so that could be point A. So, I like that choice.